The vertex form of a quadratic function is given by: y = a(x - h)² + k, where (h, k) represents the coordinates of the vertex.
Given that the vertex is at (0, 2), the equation becomes: y = a(x - 0)² + 2, which simplifies to y = ax² + 2.
Now, since the function passes through the point (3, 1), we can substitute x = 3 and y = 1 into the equation to solve for 'a':
1 = a(3)² + 2
1 = 9a + 2
Subtracting 2 from both sides gives:
-1 = 9a
Dividing by 9 yields:
a = -1/9
Therefore, the value of 'a' in the function y = ax² + c with a vertex at (0, 2) and passing through the point (3, 1) is -1/9.
